Quantum optimizer's behavior clearly isn't classical.

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Quantum optimizer manufacturer D-Wave Systems has been gaining a lot of traction recently. They've sold systems to Lockheed Martin and Google, and started producing results showing that their system can solve problems that are getting closer to having real-life applications. All in all, they have come a long way since the first hype-filled announcement.

Over time, my skepticism has waxed and waned. Although I didn't really trust their demonstrations, D-Wave's papers, which usually made more limited claims, seemed pretty solid. Now, there is a new data point to add to the list, with a paper claiming to show that the D-Wave machine cannot be doing classical simulated annealing.

Once again in English, please

Annealing is a process where you carefully and slowly allow a physical system to relax. As it's relaxing, it will carefully arrange itself so that it has the lowest possible amount of energy, called the ground state.

An example of this is a set of magnets. Each magnet can arrange itself so that it is either pointing up or down. At high temperatures (in other words, way above the ground state), each magnet arranges itself randomly, either pointing up or down. And, because the energy difference between the two states is small, they flip up and down in response to tiny changes in the local magnetic field (caused by neighboring magnets flipping).

As the magnets are cooled down, the rate of flipping slows down; however, as that occurs, the influence of the direction of the neighboring magnets becomes more substantial. In this case, where the only magnetic field is due to the magnets themselves, they start to pair up to minimize their total joint energy and reduce the total magnetic field to zero. That is, each magnet tries to minimize its energy with respect to its surroundings.

This process, called annealing, can also be simulated using a computer, and is a pretty nice way to solve some very complicated problems. But simulated annealing is, in principle, no faster than any other classical mechanism for calculating solutions to problems—although it may be more convenient to implement and optimize, and be faster in practice.

The relevance to D-Wave?

D-Wave's computer pretty much does this. They use superconducting loops to generate tiny individual magnets where the orientation depends on the direction in which the current circulates. These tiny magnets are coupled to each other so that their orientations influence each other.

To solve a problem with this bunch of magnets, however, you need to rewrite the problem so that its solution is the magnets' lowest energy state. To get there, the magnet's orientations are initialized in a well understood way, and the system is placed in the ground state for that configuration. Slowly, the environment around the magnets and coupling among them is modified so that it resembles the problem. If that is done correctly, the magnets may change their orientations, but never leave the ground state. By reading out their final orientations, you obtain the solution to the problem you wanted.

If this happens to be a classical process—which we just discussed above—then this is no faster than a classical computer. However, if the magnetics are behaving in a quantum manner, then it might be a quantum computer and could be faster.

So, is it quantum or not?

According to a recent paper in Nature Communications, the D-Wave device is not doing classical simulated annealing. Which, unfortunately, means exactly that. It tells us what it isn't, but doesn't tell us what it is.

To go into this a little more deeply, the researchers analyzed how the coupling between the magnets created a ground state. The layout of the hardware consists of four inner magnets arranged in a diamond (so each magnet is coupled directly to two others). Each of these is coupled to one additional magnet, but those are not coupled to each other. This configuration appears to be set up such that the four inner magnets always have the same orientation, while the outer magnets are free to arrange themselves as they see fit.

This results in a rather strange set of 17 possible ground states, most of which can be reached in steps of single flips of magnets. Except for the last, which requires that all four inner magnets flip at the same time.

In a classical simulation, the set of magnets can sample many different states. But, if by chance it happens to flip into this last ground state, it becomes trapped there. Furthermore, once it is there, the outer magnets become trapped in a single state too, because all other configurations have higher energy. Of course, once in this isolated state, it can also get out by flipping all four inner magnets, but the isolation and lack of noise (the outer magnets can't flip either) mean that it is, in some sense, less likely to flip out of the state than into it.

In the quantum description of these events, this doesn't happen. After setting up the ground state, we start trying to move to the solution state (by varying the environment). As soon as we do that, the ground state splits up, and the isolated state where things get stuck raises up in energy, away from the ground state. Since everything is kept in the ground state, it is no surprise that we find that the probability of entering the isolated state reduces sharply.

But, notice that this is different from the classical case. In the classical case, there was no way to break up the ground state. In other words, the energetic descriptions of the classical and quantum ground states are not the same, and it is no surprise that they give two different results.

Why the difference?

At heart, this difference was inevitable. When you get right down to it, we live in a quantum world, and if you are careful enough, that will shine through. In some ways, this shows how sloppy our thinking about the whole thing is. When we think of simulated annealing, or anything else like this, we imagine a purely classical or a purely quantum system. In reality, things are a lot more messy, with some aspects remaining classical and others showing their quantum nature.

What these results show is that we can't treat the D-Wave optimizer as a purely classical device. But, whether that actually means anything in practice is very hard to tell. One of the things that I admire about this, though, is the way the research output is slowly piling up, with much of the evidence being positive for D-Wave. It is the best way to answer critics, both professional and amateur: keep generating evidence and data.

Promoted Comments

What sort of problems could be solved by using/reading the ground state of magnets?

Any kind of problem where you have to take into account many variables and minimize some overall cost function. For example, let's say we are designing a suspension bridge. There is a single support tower in the middle, the body of the bridge itself, and the major support truss that goes from the top of the tower to the ends of the bridge body. The major truss is attached to the body by a series of minor vertical trusses. The placement of the minor trusses is not trivial - we can vary their spacing, thickness, material, tension, and so forth. There can be hundreds of minor trusses. An analytical solution may be completely intractable. A simple gradient descent optimizer will probably be unstable, and likely won't even find the most optimal solution, instead getting stuck in a local minimum somewhere. Simulated annealing can avoid local minima, and can generally deal with huge variable spaces.

As long as you can abstractly represent the original problem as a distribution of magnetic spins, this is applicable to anything.

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Chris Lee
Chris writes for Ars Technica's science section. A physicist by day and science writer by night, he specializes in quantum physics and optics. He Lives and works in Eindhoven, the Netherlands. Emailchris.lee@arstechnica.com

My question about D-Wave has always been: "How do you imagine (invent, conjure) quantum 'problems' in anything other than a classical sense?" As noted, annealing is not immune to classical solution and application, therefore, its solution cannot be strictly quantum since obviously it is not a strictly quantum problem to begin with. There are various ways in which you can "go around your elbow to get to your nose," so to speak (the long way around) in defining and solving a problem. How this relates to quantum behavior is the question--as it would seem it does not.

What sort of problems could be solved by using/reading the ground state of magnets?

Of the 'real world' problems, optimising packet and connection routing is of interest to Google; probably the reason why they wanted one of these machines. On Google scales, optimising their routes is money in the bank.

My question about D-Wave has always been: "How do you imagine (invent, conjure) quantum 'problems' in anything other than a classical sense?" As noted, annealing is not immune to classical solution and application, therefore, its solution cannot be strictly quantum since obviously it is not a strictly quantum problem to begin with. There are various ways in which you can "go around your elbow to get to your nose," so to speak (the long way around) in defining and solving a problem. How this relates to quantum behavior is the question--as it would seem it does not.

What sort of problems could be solved by using/reading the ground state of magnets?

Any kind of problem where you have to take into account many variables and minimize some overall cost function. For example, let's say we are designing a suspension bridge. There is a single support tower in the middle, the body of the bridge itself, and the major support truss that goes from the top of the tower to the ends of the bridge body. The major truss is attached to the body by a series of minor vertical trusses. The placement of the minor trusses is not trivial - we can vary their spacing, thickness, material, tension, and so forth. There can be hundreds of minor trusses. An analytical solution may be completely intractable. A simple gradient descent optimizer will probably be unstable, and likely won't even find the most optimal solution, instead getting stuck in a local minimum somewhere. Simulated annealing can avoid local minima, and can generally deal with huge variable spaces.

As long as you can abstractly represent the original problem as a distribution of magnetic spins, this is applicable to anything.

What sort of problems could be solved by using/reading the ground state of magnets?

Any kind of problem where you have to take into account many variables and minimize some overall cost function. For example, let's say we are designing a suspension bridge. There is a single support tower in the middle, the body of the bridge itself, and the major support truss that goes from the top of the tower to the ends of the bridge body. The major truss is attached to the body by a series of minor vertical trusses. The placement of the minor trusses is not trivial - we can vary their spacing, thickness, material, tension, and so forth. There can be hundreds of minor trusses. An analytical solution may be completely intractable. A simple gradient descent optimizer will probably be unstable, and likely won't even find the most optimal solution, instead getting stuck in a local minimum somewhere. Simulated annealing can avoid local minima, and can generally deal with huge variable spaces.

As long as you can abstractly represent the original problem as a distribution of magnetic spins, this is applicable to anything.

What sort of problems could be solved by using/reading the ground state of magnets?

Any kind of problem where you have to take into account many variables and minimize some overall cost function. For example, let's say we are designing a suspension bridge. There is a single support tower in the middle, the body of the bridge itself, and the major support truss that goes from the top of the tower to the ends of the bridge body. The major truss is attached to the body by a series of minor vertical trusses. The placement of the minor trusses is not trivial - we can vary their spacing, thickness, material, tension, and so forth. There can be hundreds of minor trusses. An analytical solution may be completely intractable. A simple gradient descent optimizer will probably be unstable, and likely won't even find the most optimal solution, instead getting stuck in a local minimum somewhere. Simulated annealing can avoid local minima, and can generally deal with huge variable spaces.

As long as you can abstractly represent the original problem as a distribution of magnetic spins, this is applicable to anything.

Exactly, although I would think binary computing would be far more efficient at those tasks. Ties in with my earlier comment--neither 'problem' that you mention here is or can be defined as a strictly 'quantum problem,' thus how is a device that solves classical problems not in and of itself a classical device--albeit simply a much more inefficient classical device than is currently known? (You can probably guess my amateur status here fairly easily.) It has always seemed to me that D-Wave is simply a "classical device in search of a quantum solution" as flipping magnets is more complex than flipping binary switches, but not necessarily any different. (Just less efficient, etc.)

Strictly speaking, every problem is just a mathematical one, and mathematics doesn't care whether a thing is quantum or not - it's only a matter of which equations we pick to describe the problem. The point is how we perform the computation.

Optimization is one area where a quantum computation can be much faster than a classical one. It does not matter what is being optimized - a bridge is a decidedly classical object.

I get that quantum methods can be superior for some problems, and I can buy that these would overlap with the high-dimensionality optimization problems like traveling salesman and truss placement. What I don't get is how such a problem can be represented with 17 states, one of which is forbidden, giving us four real bits.

What sort of problems could be solved by using/reading the ground state of magnets?

Simulated annealing is a general-purpose optimization method, so the sort of problems that you can apply to it is quite large. If you're Lockheed Martin you might use an optimizer to help you design an airplane (or satellite, or whatever) that weighs less but can still perform to specification, since weight is often the attribute that has the highest impact on operational cost.

I get that quantum methods can be superior for some problems, and I can buy that these would overlap with the high-dimensionality optimization problems like traveling salesman and truss placement. What I don't get is how such a problem can be represented with 17 states, one of which is forbidden, giving us four real bits.

Two bits doesn't get you much necessarily. However, performance in 2 bits exhibiting quantum behavior is indicative of the behavior of larger numbers. Moving to N- bits the assumption is that you can minimize some cost function of usefulness while still maintaining quantumness in the convergence of the solution.

I wouldn't want to fly in a plane designed by the method your example suggests. In certain situations you want to have wider fault tolerances in design - otherwise you get the M16 1st year in Vietnam scenario.

It seems plausible that even if you want to build extra safety margin into your system, you can still benefit from starting from the "optimal" solution, and working from there. Alternatively, you might be able to build the margins you want into the original problem.

Regardless of the technique, I don't think you want your safety margins to be an artifact of the fact that you were unable to find the optimal solution to a problem, so there is probably some extra play in there somewhere.

I doubt bees are really SOLVING the travelling salesman, so much as rapidly finding a "good enough" solution that puts their trip within spitting distance of best.

In the real world perfect is seldom as useful as good enough and NOW.

Of course it is possible that their tiny dedicated brain hardware has some cool quantum effect hidden... we do live in a quantum world as the article says.

In a similar way I suspect D-Wave is using approximate solutions to help speed up the calculation. Then again a quantum optimizer will in some sense be approximate, as the outcome of any calculation is probabilistic.

What sort of problems could be solved by using/reading the ground state of magnets?

Simulated annealing is a general-purpose optimization method, so the sort of problems that you can apply to it is quite large. If you're Lockheed Martin you might use an optimizer to help you design an airplane (or satellite, or whatever) that weighs less but can still perform to specification, since weight is often the attribute that has the highest impact on operational cost.

The real question (to me) is, does the D-Wave outperform a classical optimizer solving the same problems?

I wouldn't want to fly in a plane designed by the method your example suggests. In certain situations you want to have wider fault tolerances in design - otherwise you get the M16 1st year in Vietnam scenario.

If you think engineers don't apply fault tolerances to their designs (even when using optimization methods like simulated annealing), you are woefully misinformed.

The good news is that D-Wave isn't promoting a digital quantum computer, which at best has a square root speed up on generic problems (but does a bit better on specialized ones). Such computers will always be too expensive for most customers.

The bad news is that D-Wave is promoting an analog quantum computer, which may have a hefty speed up on minimization problems. Such computers will always be too limited for most customers.

I am finding the idea of quantum computing to fascinating. Aren't the types of problems quantum computing is supposed to be better for solving, not of the type present-day engineering solves? Aren't they more the types of problems that deal with complexity, the sort of problem they deal with at The Santa Fe Institute? Won't quantum computing be less of a replacement for the Von Neumann architecture and more of a complement?I'm sure quantum computing will find its uses in engineering and also in finance. I have to wonder what the Quants on Wall Street will come up with. And If its strength lies in optimization, I wonder if central banks may use it for Prisoner Dilemma types of problems and use it for setting exchange rates and money supplies. Some great comments so far, I'm learning a lot from them.

The good news is that D-Wave isn't promoting a digital quantum computer, which at best has a square root speed up on generic problems (but does a bit better on specialized ones). Such computers will always be too expensive for most customers.

The bad news is that D-Wave is promoting an analog quantum computer, which may have a hefty speed up on minimization problems. Such computers will always be too limited for most customers.

Lose-lose.

Given the subject matter in this instance wouldn't this just be "news"?

Maybe its just the problems I tend to work on, but I've never been much of a fan of metaheuristics like this. They can never give you any guarantee of convergence, and extremely finicky in that they have several parameters that are opaque to the user -- that is, they give you a bunch of adjustment knobs, but you have no idea what those knobs actually do. Further, they function only as a "black box", where they may or may not spit out a solution eventually, but they don't give you any insight into the problem itself.

"As soon as we do that, the ground state splits up ... Since everything is kept in the ground state ... In the classical case, there was no way to break up the ground state."

I fell over these words. I understand what each one means, but not these sentences. I understood the earlier explanation of what a ground state is, i.e. a low energy situation, but I can't make the jump to conceiving of what the quote is describing.

Like a good little boy, I even googled 'split the ground state', but all I got was stuff about hyperfine splitting of hydrogen atoms, which wasn't much help.

What I don't understand is how the functioning of this device can be so poorly understood. Why does all the news about it make it sound like it's a mystery box, and not something that a bunch of engineers at D-Wave designed and built?

I realize I have asked a question that opens the door to lots of clever jokes about the uncertain nature of quantum mechanics.

What I don't understand is how the functioning of this device can be so poorly understood. Why does all the news about it make it sound like it's a mystery box, and not something that a bunch of engineers at D-Wave designed and built?

I realize I have asked a question that opens the door to lots of clever jokes about the uncertain nature of quantum mechanics.

The "is it classical or quantum" argument is really a smoke screen covering the real argument: "is it any faster than just running classical computations on a GPU cluster?"

The answer so far has been "no".

Someone correct me if I'm wrong, but I believe this is how the debate over the quantum nature lays out:

It would be possible to run a processor similar to DWave's that has no quantum effects going on within it (just little magnets flipping around like described in the article). Since a final result is based on a statistical analysis of repeated runs of the same initial condition, you might get very similar answers using a classical setup. But the quantum setup should converge on a solution faster and with more accuracy than the classical setup would. But since we don't have a "perfectly classical" or "perfectly quantum" version to compare this to, then it's actually kind of hard to figure out how much quantumness is going on in there just by looking at the results.

So the guys referenced in the article have actually shown that hard thing -- that the results they are seeing in some special case could only be the result of some kind of quantum effect occurring (probably "only" is overstated... they are probably applying a statistical test like "95% certainty that the results are consistent with quantum and not classical effects").

But, as I opened this post with, there's still lots of people whose response to that is "cool... but are they getting faster computation out of it?"

It should be noted that few (if any) of the critics I've read online think that DWave isn't pushing the science of quantum computing forward with what they're doing. There's just a question of whether they have a product that is superior to competitors (i.e. GPU clusters) or whether this is just cool science. But everyone seems to agree it's at least cool science.

"As soon as we do that, the ground state splits up ... Since everything is kept in the ground state ... In the classical case, there was no way to break up the ground state."

I fell over these words. I understand what each one means, but not these sentences. I understood the earlier explanation of what a ground state is, i.e. a low energy situation, but I can't make the jump to conceiving of what the quote is describing.

Like a good little boy, I even googled 'split the ground state', but all I got was stuff about hyperfine splitting of hydrogen atoms, which wasn't much help.

Well, there are 2 theories describing reality, your 'classical' description of reality (where everything has a well defined location&speed and things are generally always predictable, or at least simulate-able), and your 'quantum' description of reality (where everything is essentially a superposition of energy wave-forms, nothing has well defined location&speed, and everything behaves according to probability so cannot be specifically predicted).

What this sentence is saying (as I understand), is that the classical model of this setup of magnets will not allow for the magnets to ever come out of the ground state, because the equations describing the arrangement prove that the magnets cannot leave this 'classical ground state'. But, in the quantum model of this setup, the magnets are able to rearrange themselves (after the environment is altered) because they are able to manifest behavior of the wavy, probabilistic nature of quantum reality.

Look up quantum tunneling, I'm guessing this is essentially the same principle. In a classical description of a ball sitting in a container, the ball can never leave the container. But in the quantum description, it can magically jump outside the container! This only happens at the very small level of course.

So, to summarize, the magnets can 'sense' the new ground states because at a very small level everything is just a manifestation of energy wave functions that behave according to probability, and not strictly cause and effect. This is probably a horrible simplification but that's how i interpret it